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  3. In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n, ∠ACB has a measure

In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n, ∠ACB has a measure

游客2025-02-27  16
问题 In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n, ∠ACB has a measure of n, and ∠DBC has a measure of 45°, what is the measure of ∠ABC? (Figure not necessarily drawn to scale.)
选项 A、45°
B、60°
C、90°
D、105°
E、120°
答案 D
解析 The principle to remember here is that an exterior angle of a triangle--such as ∠ADB--is equal to the sum of the remote interior angles of the triangle, in this case ∠DBC and ∠DCB (=∠ACB) of triangle BDC. Thus, ∠DCB+∠DBC=4n, or ∠DBC=3n=45°, and therefore n=15° and 4n=60°. The three angles of a triangle must equal 180°, so ∠ABC=180°-60°-15°=105°.
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